91Ó°ÊÓ

When solving a linear equation, the first step often involves combining like terms. Like terms are terms in an equation that have the same variables raised to the same power. For instance, in the equation \(5x + 4 - 4x = 0\), the like terms are \(5x\) and \(-4x\). Combining them means you simply add or subtract their coefficients (the numbers in front of the variables).

In our example, combining \(5x\) and \(-4x\) gives \((5x - 4x) = x\).

By doing this, we simplify the equation to \(x + 4 = 0\).

This step is essential because it reduces the equation to a simpler form, making it easier to solve. Always look for like terms to combine first to streamline the equation.

After combining like terms, the next step in solving a linear equation is to isolate the variable. Isolating the variable means getting the variable alone on one side of the equation. This often involves performing algebraic operations such as addition, subtraction, multiplication, or division.

In our equation \(x + 4 = 0\), we want to get \(x\) by itself. To do this, we subtract 4 from both sides of the equation:
\(x + 4 - 4 = 0 - 4\).

This simplifies to \(x = -4\).

By isolating the variable, we find that \(x = -4\).

This step is critical because it allows you to solve for the variable directly, giving you the solution to the equation.

The final step in solving a linear equation is to check the solution. Checking the solution means substituting the value you found for the variable back into the original equation to ensure it balances (both sides of the equation equal each other).

In our example, the original equation is \(5x + 4 - 4x = 0\). We found that \(x = -4\).

To check this, substitute \(x = -4\) back into the equation:
\(5(-4) + 4 - 4(-4) = 0\).
This simplifies to \(-20 + 4 + 16 = 0\).

Combining these, we have \(0 = 0\), which is true. Hence, \(x = -4\) is the correct solution.

Always check your solution to confirm accuracy. It's an invaluable step to ensure you didn't make any mistakes during the solving process.